Towards Inference-time Scaling for Continuous Space Reasoning

2025-10-14

AI Summary

This work investigates whether inference-time scaling techniques—such as multi-path sampling and reward-model re-ranking—can effectively transfer to continuous thought spaces. Methodologically, building upon the COCONUT framework, it employs dropout-driven diverse reasoning path generation and integrates both process-based (PRM) and outcome-based (ORM) reward models for re-ranking. Geometric analysis and trajectory dynamics probing further reveal that the fundamental challenge in continuous spaces—indistinguishability between correct and incorrect reasoning—stems from insufficient discriminative structural priors in current representations. The core contribution is threefold: (1) the first systematic validation of multi-path sampling feasibility in continuous reasoning spaces; (2) identification that gains from discrete-space paradigms are fundamentally limited by weak representation discriminability; and (3) a novel direction advocating explicit injection of discriminative structural priors during training. Experiments confirm that while current methods improve Pass@N, the bottleneck lies at the representational level—not the search strategy.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Sequential Decision Making
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Inference-time scaling through multiple sample generation in combination with Process- or Outcome-Reward Model (PRM or ORM) re-ranking has proven effective for text-based reasoning in large language models. This paper investigates whether such established techniques can be successfully adapted to reasoning in the continuous space, using COCONUT (Hao et al. 2024) continuous space reasoning LM as the backbone. We demonstrate the feasibility of generating diverse reasoning paths through dropout-based sampling. Our Pass@N analysis on the generated samples reveals the potential that could enable a significant gain in performance akin to observed gain in the discrete space. However, we highlight unique challenges faced for materializing this gain in the continuous thought space. In particular, working recipes for data generation and training PRM and ORM models in the discrete space unlocks only marginal improvements in the continuous space. Through probing various aspects including geometric properties and trajectory dynamics we identify the underlying reasons that prevent effective discrimination between correct and incorrect reasoning (essential for the functioning of PRM and ORM). Our findings reveal that current limitations stem from the absence of key inductive biases in continuous thought representations. We argue that the training frameworks for continuous reasoning LMs require not only to optimize for accuracy but also to explicitly incorporate inductive biases that could be utilized during inference-time for discrimination of correct and incorrect thoughts.footnote{Our code and data will be publicly available.}

Problem

• Adapting inference-time scaling techniques to continuous space reasoning
• Investigating challenges in discriminating correct vs incorrect continuous reasoning paths
• Addressing limitations in inductive biases for continuous thought representations

Innovation

• Uses dropout sampling for diverse reasoning paths
• Applies PRM/ORM re-ranking in continuous space
• Identifies need for inductive biases in training